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A theory of fractional integration for generalised functions II*

Published online by Cambridge University Press:  14 February 2012

Adam C. McBride
Adam C. McBride
Affiliation:
Department of Mathematics, University of Strathclyde
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Synopsis

In a previous paper [2], a theory of fractional integration was developed for certain spaces Fp,μ of generalised functions. In this paper we extend this theory by relaxing some of the restrictions on the various parameters involved. In particular we show how a generalised Erdelyi-Kober operator can be defined on Fʹp,μ for 1 ≦ p ≦ ∞ and for all complex numbers μ except for those lying on a countable number of lines of the form Re μ = constant in the complex μ-plane. Mapping properties of these generalised operators are obtained and several applications mentioned.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 3-4 , 1977 , pp. 335 - 349
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Kober, H.. On fractional integrals and derivatives. Quart. J. Math. Oxford Ser. 11 (1940), 193–211.CrossRefGoogle Scholar
2McBride, A. C.. A theory of fractional integration for generalised functions. SIAMJ. Math. Anal. 6 (1975), 583–599.CrossRefGoogle Scholar
3McBride, A. C.. Solution of hypergeometric integral equations involving generalised functions. Proc. Edinburgh Math. Soc. 19 (1975), 265–285.CrossRefGoogle Scholar
4McBride, A. C.. A note on the spaces Fʹp,μ. Proc. Roy. Soc. Edinburgh Sect. A 11 (1977), 39–47.CrossRefGoogle Scholar
5Sneddon, I. N.. Mixed boundary value problems in potential theory (Amsterdam: North-Holland 1966).Google Scholar
6Zemanian, A. H.. Generalized integral transformations (New York: Interscience, 1968).Google Scholar
7Erdelyi, A.. On fractional integration and its application to the theory of Hankel transforms. Quart. J. Math. Oxford Ser. 11 (1940), 293–303.CrossRefGoogle Scholar